Phased array antenna

ABSTRACT

A phased array antenna device including a plurality of equally spaced antenna elements which are connected to a source of antenna power, and a plurality of impedance transforming four terminal networks capable of electrically adjusting the radiation characteristics of the antennas by varying the phase and amplitude of the antenna currents in a predetermined manner.

United States Patent [72] inventors Kiyoshi Nagai;

Torao Nagai; Sohii Okamura, all of Yokohama-shi, Japan [21] Appl/No. 866,212

[22] Filed Oct. 14, 1969 [45'] Patented Oct. 5, 1971 [73] Assignee Tokyo Shibaura Electric Co., Ltd.

Kawasaki-shl, Japan [32] Priority Oct. 16, 1968 [54] PHASED ARRAY ANTENNA 14 Claims, 19 Drawing Figs.

[52] U.S. Cl 343/844, 343/854 [51] lnt.C1 H0lq 3/26, l-lOlq 21/00 [50] Field of Search ..343/777-778,

[56] References Cited UNITED STATES PATENTS 3,160,887 12/1964 Broussaud et a1 343/777 3,230,539 1/1966 Schell 343/854 3,246,265 4/1966 Smith-Vaniz.. 333/31 3,260,968 7/ 1 966 Drapkin 333/29 3,435,453 3/1969 l-loward.. 343/777 X 3,478,358 11/1969 Trigon.... 343/854 X 3,478,359 11/196 9 Salmon 343/854 X OTHER REFERENCES Microwave Scanning Antennas- Hansen (Volume 1 l l-Array SystemsiAcademic Press- New York TK 7872 A6 H33 pages 5-9 and 110-114 I A Very Fast, Voltage-Controlled, Microwave Phase Shifter-Dawirs and Swarner in The Microwave Journal" June 1962 Vol. V, No.6 TX 7800 M5 pages 99-106 Primary ExaminerEli Lieberman Assistant Examiner--Marvin Nussbaum Attorney-Flynn and F rishaut' ABSTRACT: A phased array antenna device including a plurality of equally spaced antenna elements which are connected to a source of antenna power, and a plurality of impedance transforming four terminal networks capable of electrically adjusting the radiation characteristics of the antennas by varying the phase and amplitude of the antenna currents in a predetermined manner,

PATENTEU 0m 51% 3,611,400

saw u 0F 4 Fl G. 13 FIG. 14

1.1 u 1 13 1.2 1.1 l3 I3=O 1.2 11F? 2 15 11 11 W; W5

FIG. 15 FIG. 16

2.1 22 2.1 12=O V 22 Q V4 V 23 2 .14 v4 PHASE!) ARRAY ANTENNA This invention relates to an improved phased array antenna device comprised by an assembly of a plurality of antenna elements, and more particularly to a phased array antenna device suitable for use as an antenna mechanism for radar communication and artificial satellite communication.

Prior art phased array antenna devices of this type which have been put into practical use are ordinarily constructed as shown in FIG. 1, in the case of the parallel feed system for example. Thus, for example, denoting the number of antenna elements by r, respective antenna elements 11,, 11 ll:,,..., 1 I, are connected in parallel to a common source of antenna power I2 through a feeder 13 consisting of two parallel lines or-a coaxial line, said antenna elements being spaced each other with equal spacings d. In this case, phase shifters 14 14,, 14,, I4, are connected in series with respective antenna elements 11,, I1 II, at their feeder terminals to cause the phases of currents flowing through respective antenna elements to successively differ by 2"", e e e""""9, where k=21r/A, where A represents the wavelength of the antenna current supplied from the source of antenna power 12 so that directions of scanning (in this case in the direction of of respective radiated beams of electromagnetic waves as viewed from the boresight of respective antenna elements substantially coincide.

We have found that with such a prior phased array antenna device, however, unless suitable impedance matching is provided for respective antenna elements, very complicated interference phenomena are created between respective antenna elements so that it is not only difficult to cause to precisely coincide all directions of scanning of the beams of radiated electromagnetic waves from respective antenna elements, but also characteristics of the beams of the radiated electromagnetic waves are distorted to degrade the S/N ratio. Such phenomena are remarkable especially when the load (in this case respective antenna elements) changes or the frequency of the antenna current fed from the source of the antenna power varies. 158 To obviate these defects, impedance matching devices as shown in FIGS. 2A to FIG. 4 have been proposed in the past. Thus, where the feeder adapted to connect the source of antenna power l2 to antenna elements 11,- I l, is comprised by a pair of parallel lines 13a as shown in FIG. 2A or by a coaxial line 13b including an outer conductor 13,, and an inner conductor 13,, as shown in FIG. 28, an impedance matching stub 21,, including similar parallel lines with their ends short circuited or an impedance matching stub 21b including a coaxial line with the ends of its outer and inner conductors short circuited is connected to a suitable point along the length of the feeder 13,, or 13,, and the length l of the stub 21,, or 21,, to the short circuited ends is adjusted in the following manner. As shown in FIG. 3 where the impedance matching stub is in the form of the coaxial line 21,, including an outer conductor 21,, and an inner conductor 21 the coaxial line is made hollow with its outer end opened and to have a length of more than one-half of the wavelength of the antenna current. A movable short-circuiting member 22 made of a conductor and having a length of more than one-half of the wavelength of the antenna current is inserted into the stub through its opened end and the short-circuiting member is mechanically adjusted in the direction of an arrow 23 or 24. Such mechanically operated impedance matching means not only requires troublesome operation but also is difficult to adjust quickly in response to variations in the load and antenna current frequency. Further, where such a single-impedance matching stub is provided for each antenna element it is necessary to cut the antenna feeder at each point where such stub is connected. To avoid such inconvenience, three stubs spaced apart from each other by one-fourth wavelength have been connected to the feeder. Although this solution is advantageous in that it is possible to provide the required matching irrespective of the length between the points of insertion of the stubs and the load, adjustment of impedance matching becomes more troublesome.

Another means of the prior art for matching impedance consists of a two-inner conductor matching device, as shown in FIG. 4, wherein use is made of a twocore coaxial line 13,. comprising an outer conductor 13 and two-inner conductor conductors 13, and 13 with their one ends bent as shown- These inner conductors are short circuited by means of a conductive short-circuiting plate A at a distance I from the bent ends whereas the inner conductors and the outer conductor 13,, are short circuited by means of a conductive short-circuiting plate B at a distance 1 from the bent ends, said short-circuiting plates A and B being mechanically adjustable independently. However, such a matching device requires more complicated adjustment than those shown in FIGS. 2A and 25.

Furthermore, each of these prior art impedance matching devices is effective only for the variations in the load and is not effective for the variations in the direction of scanning of the beams of electromagnetic waves radiated from respective antenna elements. For this reason, it has been necessary to use phase shifters as above described.

Accordingly, it is an object of this invention to provide a new and improved phased array antenna device wherein the directions of scanning of the beams of electromagnetic waves radiated from respective antennas can be rapidly and smoothly adjusted by electric means which controls the fed terminal voltage of respective antenna elements.

According to this invention, there is provided a phased array antenna device comprising a source of antenna power, a plurality of antenna elements connected to said source at equal spacings, and an impedance transforming four-terminal network connected between each antenna element and said source such that the direction of scanning of the beam of the electromagnetic wave radiated from each antenna element and the voltage of said beam can be varied electrically.

This invention can be more fully understood from the following detailed description when taken in connection with reference to the accompanying drawings, in which:

FIG. 1 is a schematic representation of a prior art phased array antenna device;

FIGS. 2A and 2B are diagrams of prior art impedance matching mechanisms that can be employed in the phased array antenna device shown in FIG. I;

FIG. 3 shows a detailed construction of the impedance matching mechanism shown in FIG. 28;

FIG. 4 diagrammatically shows another example of the prior art impedance matching mechanism usable for the phased array antenna device shown in FIG. 1;

FIG. 5 is a diagram of a phased array antenna device embodying this invention;

FIG. 6 and 7 show different types of the impedance transfonning four-terminal networks utilized for the phased array antenna device as shown in FIG. 5;

FIG. 8 shows one embodiment of the impedance transforming four-terminal network actually employed in the phased array antenna device shown in FIG. 5;

FIG. 9 is a Smith chart illustrating the impedance variation of the impedance transforming four-terminal network shown in FIG. 8;

FIGS. 10 and 11 shown other examples of impedance transforming four-tenninal networks;

FIGS. 12A and 128 show modified embodiments wherein the distributed constant line shown in FIG. 11 is substituted by concentrated constant lines;

FIGS. 13 to 16 show different examples of two wire lines of distributed constant; and

FIG. 17 shows still another embodiment of the impedance transforming four-terminal network comprising a suitable combination of lines shown in FIGS. 13 to 16.

The outline of the construction of the phased array antenna device will be given with reference to FIGS. 5 to 7. Like the arrangement shown in FIG. 1 a plurality of antenna elements 33,, 33 33,,...33,,, are connected in parallel to a source of antenna power 31 through a junction box 32, said antenna elements being spaced from each other by equal spacings d to form a phased array antenna device. In accordance with this invention, between feed ends of antenna elements 33,, 33 33 ,...33 and the junction box 32 are included impedance transforming four-terminal networks 34,, 34 ,...34 having characteristics to be described hereunder. If desired, a similar impedance transforming four-terminal network 35 may be connected between the junction box 32 and the source 31.

Here all antenna feeder lines between the junction box 32 and the input terminals of the respective impedance transforming four-terminal networks 34,-34,,,,, are made to have an equal length kJtg by being provided with additional windings W,, W Also, all antenna feeder lines between the output terminals of the respective impedance transforming four-terminal networks and the feed terminals of the corresponding antenna elements 33 33,,, are made to have an equal length p. \g as shown in FIG. 5. k and p are integers, and Ag is the wavelength of the antenna current in the antenna feeder lines.

Considering now a column matrix [I] of the antenna current fed to respective antenna elements 33,,...33,,, from the source 31 through the junction box 32, from foregoing description, to scan antenna beams from each of the antenna elements in the 6,, direction, the following relation should hold.

iII jAi-IWI where l =(21r/)\)'d-sin6 and 0, represents the amplitude ratio for the ith antenna element 33i which is determined from the sidelobe level requirement, and I, is the current fed to the first antenna element 33,.

Considering an m row, m column matrix [Z] for the selfradiation impedance and the mutual radiation impedance between m antenna elements and a column matrix [V] for the feed terminal voltage of respective antenna elements 33,,...33,,, the following equations hold.

In equation (2),

where Z, (i k) represents the mutual radiation impedance between ith and kth antenna elements and Z,, the self-radiation impedance of the ith antenna element.

Accordingly, the feed terminal voltage V, of the ith antenna element 33, required to feed an antenna current I, C'ili-UQS to it through impedance transforming four-terminal networ 34, can be derived as follows from equation (2).

Taking the current I, flowing through the first antenna element 33, as the reference, equation (3) becomes:

Substituting equation (6) into equation (4), we obtain Accordingly, the impedance Z, of the ith antenna 33, is expressed by Therefore the I, to be fed to the ith antenna element 33, is expressed by Thus the phased array antenna device can be constructed by connecting impedance transforming four-terminal networks 34,,...34,,,,, between feed terminals of respective antenna elements 33 ,...33 and the junction box 32, the output voltage of said networks satisfying the relation of V, expressed by equation (7) when the input terminal voltage equals V In order to make the voltage impressed upon the input terminals of respective impedance transforming four-terminal networks 34,,...34,,,,, from the source of antenna power 31 through junction box 32 to be equal to V,,, it is necessary to select the length of feeder lines between the junction box and respective networks to be equal to integer multiples of the wavelength Ag of the antenna current from the antenna power source 31; because all antenna elements are fed in parallel from the same source 31. This means that the same voltage at the junction box is applied to the input terminals of the impedance transforming four-terminal networks 34 ,,...34,,,,,.

Examples of impedance transforming four-terminal networks 34,,...34,,,,, suitable for use in practical applications are described below.

Where each of the impedance transforming four-terminal networks 34,,...34,,,,, is comprised by two parallel reactance Similarly, where each of the impedance transfonning fourterminal networks 34,,...34,,,,, is comprised by three reactances X X, and X, respectively spaced by )\/4 from feed terminals 41, and 42, of two parallel feeder lines 41 and 42 to the Z, comprised by the antenna element as shown in FIG. 7, its basic chain matrix [F is expressed by Thus, in both Figs. 6 and 7 Substituting equations (6), and (7) and (9) into equation l2) Z an -jm-tldr The desired impedance transforming four-terminal network can be realized by determining values of X, and X, which are necessary to make equal the rightand left-hand terms of i i BiXi From the above equations can be determined the values ofparallel reactances X, and X and in consequence the values of the impedance transforming four-terminal circuit networks 34, to 34,,,,, according to the present invention as shown in FIGS. 6 and 7 which are used in generating a voltage V, at the output terminal of each of said networks. If, in this case, there occurs changes in the angle at which scanning is conducted by the beams radiated from the antenna elements 33, to 33,,,, then the values of X, and X, will be displaced accordingly so that it is necessary to adjust said values to the proper levels respectively which prevailed before the occurrence of such changes.

FIG. 8 illustrates one example of variable reactance elements X, and X adapted for use in a four-terminal network as shown in FIGS. 6 and 7 that can satisfy the relationship shown in FIGS. 6 and 7 and described in connection therewith wherein circuit elements 49 and 50 whose reactance can be varied electrically, such as variable capacitance diodes, are connected between one end 3, and 4, and between the other end 3 and 4 of each of two parallel lines 3 and 4 connected in parallel to a predetermined position longitudinally of feeder lines 41 and 42 leading to antenna elements 33 ,...33 said feeder lines comprising two parallel lines of M4 long. The circuit elements 49 and 50 are connected to variable DC bias sources 47 and 48, respectively, through circuit elements 43, 44, 45 and 46 which pass direct current and are included when desired. The impedance Z of diode 50 connected between output terminals, when viewed from input terminals 3, and 4, through lines 3 and 4, is expressed by llr where 2,, represents the characteristic impedance of the lines and 2 the inherent impedance of diode 50.

Considering now Z as the pure reactance 1 l ZDr mln.) (-1 max) Therefore, the admittance y corresponding to Z is exand the admittance Y by The admittance Y as seen from input terminals is given by Consequently, Y," can be gradually variable in a range of 55 l l from 1(m2 (0C,-,,,,, to (mC,,, wcmaxy 20 during 1 Y... max.=j(21r- 10 -70-10' j2.4-Q 0-j1.28Q which is impossible to realize, the result of our experiment shows that there is no fear of creating a situation in which it is impossible to match in the actual circuits. Although the standing wave ratio of the circuits deviates somewhat from 1.0 it does not cause any trouble.

In this case, by calculating beforehand the relationship between the scanning angle of the beams of electromagnetic waves radiated from various antenna elements and the bias voltage to be impressed to corresponding ones of variable capacitance diodes 49 and 50 from DC bias sources 47 and 48, it is possible to cause the DC bias sources to fully automatically, smoothly and quickly respond to variations in the load or antenna current frequency by the program control of an electronic computer system.

In this case, where the voltages applied to variable capacitance diodes 49 and 50 from DC bias sources 47 and 48 are varied in n steps it is possible to provide a digital control which varies in n n equal steps (in this example n=4) around v the periphery of a Smith chart as shown in FIG. 9.

FIG. shows another embodiment of this inventio n wherein the reactance elements X l and X (where X ,=jZ,,,,-tan [31,; X =jZ,,,,-tanBl Z characteristic impedance of balance mode; Z characteristic impedance of unbalance mode; and B wave number) of impedance transforming four-terminal network as shown in FIG. 4 are respectively comprised of a two inner conductor coaxial line 51 having two inner conductors 51 and 51 enclosed by an outer conductor 51,. Each one of inner conductors 51 and 51 of the coaxial line 51 is divided into small sections of Al along its length and direct current blocking and coupling condensers C C C, ,...and C C C mhaving sufficiently small reactance for the antenna current frequency are connected between divided sections. Across alternate sections of inner conductors 51 and 51 are connected, for example PIN diodes D D mand between outer conductor 5| and one set of alternate sections of inner conductors 51 and 51;, are connected circuit elements L L msuch as inductance coils which permit free flow of direct current but manifest sufficiently high impedance against high-frequency antenna current. One terminal of each of these circuit elements L L, ...is connected to respective DC bias sources 53,, 53 ...through perforations 52,, 52 ...in the outer conductor 51,. Across the outer conductor 51 and the other set of alternate sections of inner conductors 51 and 51 are connected PIN diodes D D mand across these sections are connected circuit elements L L msuch as inductance coils which permit free flow of direct current but manifest sufficiently high impedance against the antenna current. Similarly, one terminal of these circuit elements are connected to respective variable DC bias sources 55,, 55 ...through perforations 54,, 54 mm the outer conductor 51,. If desired, bypass condensers 56,, 56;...may be connected between DC bias sources 53 53;...and 55,, 55 ...and the outer conductor 51,, as shown in FIG. 10.

With this arrangement by applying a bias voltage to the FIN diode of any one section from the associated DC bias source in order to maintain said particular diode in short-circuited condition but to maintain other diodes in open circuited condition, it is possible to short circuit both inner conductors 51, and 51 or outer conductor 51, and both conductors at every two sections. When compared with prior impedance matching devices wherein the impedance thereof has been varied mechanically, the impedance matching network can provide faster and smoother impedance matching adjustment in response to variations in the load or antenna current.

FIG Tl S56v7; another embodimeht oft his invention wherein the reactance elements X and X of impedance transfomiing four-terminal network as shown in FIGS. 6 and 7 are comprised respectively of a feeder line 62 mounted on a grounded plate 61. Equally spaced-apart diodes 63,, 63 63 ,...are connected to the feeder line 64,, 64 64 ,...are connected between respective diodes and grounded plate 61 to form bypass paths to high-frequency transmission current. The other terminals of the condensers are connected to variable DC bias sources 65,, 65 65 With these reactance elements, since the diodes are rendered in their on or off state according to the value of bias voltage supplied thereto from corresponding DC bias sources 65 65 65 ,...either one of the diodes is rendered on while others are all in their off state. Denoting by d the length of the feeder line between its feed terminal and a point to which a diode is connected, the input reactance of this circuit is given y N Z.-..=j 5 tan/37.11 (17) where Z represents the characteristic impedance of the line and B=21r/ When another diode is rendered on while remaining diodes are off, the input reactance of the line for different lengths d can be similarly given. Thus, the input reactance can be varied by varying the spacing between diodes according to equation (17). Thus, it is possible to vary the impedance represented by the Smith chart in the same manner as above described.

In the actual construction of a circuit as shown in FIG. 11, if the line were too long it may be possible to decrease its length by replacing equivalent concentrated L, C elements for the distributed circuit constants as shown in FIGS. 13A and IZB.

FIG. 13 represents still another embodiment of the reactance elements X l and X; of the impedance transforming four-terminal network as shown in FIGS. 6 and 7. Considering two lines 1 and 2 coupled to each other by the distributed constants and having terminals (Ll). (1.2), (2.1) and (2.2) and by denoting their terminal voltages and currents by (V 1,), (V 1 (V 1 and (V 1 respectively, the fundamental equations for this eight-terminal network are given by V V3 COS Sll'l I3 Denoting the characteristic impedance of a balanced system by Z and that of an unbalanced system by Zn,

Z 00 ou where B represents the propagation constant of said two systems and l the length thereof.

If, a shown in FIG. 14, terminal (1.2) is opened, terminal (2.2) short circuited and terminal (2.1) connected to anv im- Solutions of this equation are i I,- K (cos [31+ Z2 sinpl I and the input impedance Zm of this circuit is expressed by i 1 III,

mzzzoou K*)Z%o sin 31 cos 1 22200 cos p1 As shown in FIG. 15, if an impedance Z is connected to terminal (L2), and terminals (2.1) and (2.2) are short circuited, then V Consequently, the line'functions as a transmission line having a characteristic impedance IK )Z and a length I.

When, as shown in FIG. 16, terminal (2.2) is connected to an impedance Z.,, and tenninals (1.2) and (2.1) are open following relations hold.

V1 V3 COS sin sin B] The input impedance Z1, in this case is given by This is equivalent to a case wherein impedance Z is connected to a line having a characteristic impedance K2 and a length M4.

When Z. equals infinity, 2,, becomes zero and short circuited.

Then, as shown in FIG. 17, circuits of FIGS. 14 and 16 are interconnected.

First assuming that Z, is equal to infinity, then 2' is zero, and 2' is infinity, Z is K"Z,, when Z, is varied from j to j0, 2 also changes from j to j0, Z is varied from so under short circuited condition of 2,.

If, at this time, Z is also varied from j m to j0, as has been described in connection with FIG. 15, the section connected to impedance Z, and the next succeeding section comprise a transmission line having an overall characteristic impedance Z and a length of M2 so that Z is equal to Z,,,.

If K Z /Z /2 and if Z is varied from j w to j0, from equation (3 l Z, will change from j0 to j As above described, the circuit shown in FIG. 17 provides a circuit wherein the impedance can be varied from j w to j passed through zero by varying Z. and 2 from j to j0. R If in this case, variable capacitance diodes are utilized as impedances Z, and Z and if variable DC bias voltages are applied to these diodes through grounded conductors, it is possible to provide still another reactance element for impedance transforming four-terminal network for use in this invention that can attain the same objects as the previous embodiments.

We claim:

1. A phased array antenna device comprising a source ofantenna power; a plurality of equally spaced antenna elements energized by said source; and a plurality of impedance transforming four-terminal networks, each of which is connected between said source and the feed terminals of respective antenna elements, each one of said networks being constructed to satisfy the equation:

ii-l

where:

V the voltage applied to the input terminal of said impedance transforming network,

Vi the ith output voltage appearing at the output terminal of said impedance transforming network,

Zin the self-radiation impedance and mutual radiation impedance of the ith antenna element,

Zkn the self-radiation impedance and mutual radiation impedance of the kth antenna element,

an the amplitude ration which is given from the sidelobe requirement, and

d the spacing between adjacent ones of said antenna elements,

A the wavelength of the antenna current from said source, and

6 the scanning direction of radiated beams from each of said antenna elements.

2. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises a pair of parallel lines of one-fourth wavelength connected in series with a feeder line leading to one of said antenna elements, variable reactance elements connected to the opposite ends of said parallel lines and variable DC voltages connected to said variable reactance elements.

3. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises a coaxial line connected in series with a feeder line leading to each antenna element, said coaxial line including an outer conductor and two inner conductors connected in parallel, a first group of variable reactance elements connected across said inner conductors at spaced intervals along the length thereof, a first group of variable DC bias sources connected to said variable reactance elements, a second group of variable reactance elements connected between said outer conductor and said inner conductors in an interleaved fashion with the reactance elements of said first group, and a second group of variable DC bias sources connected to said second group of reactance elements.

4. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises a line parallel to a grounded plate and connected in series with a feeder line leading to each antenna element, a plurality of variable reactance elements connected to said line at spaced intervals along the length thereof, and a plurality of variable DC bias sources connected to said variable reactance elements.

5. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises two lines of distributed constants connected in series with a feeder line leading to each antenna element, each of said lines having a length equal to one-fourth of the wavelength of the antenna current, variable reactance elements respectively connected between opposite ends of said lines, and variable DC bias sources connected to said variable reactance elements.

6. A phased array antenna device according to claim 4 wherein said lineparallel to said grounded plate of said impedance transforming four-terminal network is comprised by a line of concentrated circuit constants so as to decrease the length thereof.

7. A phased array antenna device according to claim 2 wherein said variable reactance elements comprise variable reactance diodes.

8. A phased array antenna device according to claim 3 wherein said variable reactance elements comprise diodes.

9. A phased array antenna device according to claim 4 wherein said variable reactance elements comprise diodes.

10. A phased array antenna device according to claim 5 wherein said variable reactance elements comprise diodes.

11. A phased array antenna device according to claim 2 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.

12. A phased array antenna device according to claim 3 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.

13. A phased array antenna device according to claim 4 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.

14. A phased array antenna device according to claim 5 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system. 

1. A phased array antenna device comprising a source of antenna power; a plurality of equally spaced antenna elements energized by said source; and a plurality of impedance transforming fourterminal networks, each of which is connected between said source and the feed terminals of respective antenna elements, each one of said networks being constructed to satisfy the equation: where: Vo the voltage applied to the input terminal of said impedance transforming network, Vi the ith output voltage appearing at the output terminal of said impedance transforming network, Zin the self-radiation impedance and mutual radiation impedance of the ith antenna element, Zkn the self-radiation impedance and mutual radiation impedance of the kth antenna element, an the amplitude ration which is given from the sidelobe requirement, and 0 (2 pi / lambda )od.sin theta , where: d the spacing between adjacent ones of said antenna elements, lambda the wavelength of the antenna current from said source, and theta the scanning direction of radiated beams from each of said antenna elements.
 2. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises a pair of parallel lines of one-fourth wavelength connected in series with a feeder line leading to one of said antenna elements, variable reactance elements connected to the opposite ends of said parallel lines and variable DC voltages connected to said variable reactance elements.
 3. A phased array antenna device according to claim 1 wHerein each one of said impedance transforming four-terminal networks comprises a coaxial line connected in series with a feeder line leading to each antenna element, said coaxial line including an outer conductor and two inner conductors connected in parallel, a first group of variable reactance elements connected across said inner conductors at spaced intervals along the length thereof, a first group of variable DC bias sources connected to said variable reactance elements, a second group of variable reactance elements connected between said outer conductor and said inner conductors in an interleaved fashion with the reactance elements of said first group, and a second group of variable DC bias sources connected to said second group of reactance elements.
 4. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises a line parallel to a grounded plate and connected in series with a feeder line leading to each antenna element, a plurality of variable reactance elements connected to said line at spaced intervals along the length thereof, and a plurality of variable DC bias sources connected to said variable reactance elements.
 5. A phased array antenna device according to claim 1 wherein each one of said impedance transforming four-terminal networks comprises two lines of distributed constants connected in series with a feeder line leading to each antenna element, each of said lines having a length equal to one-fourth of the wavelength of the antenna current, variable reactance elements respectively connected between opposite ends of said lines, and variable DC bias sources connected to said variable reactance elements.
 6. A phased array antenna device according to claim 4 wherein said line parallel to said grounded plate of said impedance transforming four-terminal network is comprised by a line of concentrated circuit constants so as to decrease the length thereof.
 7. A phased array antenna device according to claim 2 wherein said variable reactance elements comprise variable reactance diodes.
 8. A phased array antenna device according to claim 3 wherein said variable reactance elements comprise diodes.
 9. A phased array antenna device according to claim 4 wherein said variable reactance elements comprise diodes.
 10. A phased array antenna device according to claim 5 wherein said variable reactance elements comprise diodes.
 11. A phased array antenna device according to claim 2 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.
 12. A phased array antenna device according to claim 3 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.
 13. A phased array antenna device according to claim 4 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system.
 14. A phased array antenna device according to claim 5 wherein the bias voltages supplied to said variable reactance elements from said variable DC bias sources are varied by a program control of an electric computer system. 